Question

Two used car dealerships compete side by side on a main road. The first, Harry’s Cars, always sells high-quality cars that it carefully inspects and, if necessary, services. On average, it costs Harry’s $8000 to buy and service each car that it sells. The second dealership, Lew’s Motors, always sells lower-quality cars. On average, it costs Lew’s only $5000 for each car that it sells. If consumers knew the quality of the used cars they were buying, they would pay $10,000 on average for Harry’s cars and only $7000 on average for Lew’s cars.

Without more information, consumers do not know the quality of each dealership’s cars. In this case, they would figure that they have a 50-50 chance of ending up with a high-quality car and are thus willing to pay $8500 for a car. Harry has an idea: He will offer a bumper-to-bumper warranty for all cars that he sells. He knows that a warranty lasting Y years will cost $500Y on average, and he also knows that if Lew tries to offer the same warranty, it will cost Lew $1000Y on average.

a. Suppose Harry offers a one-year warranty on all of the cars he sells. i. What is Lew’s profit if he does not offer a one-year warranty? If he does offer a one-year warranty? ii. What is Harry’s profit if Lew does not offer a one-year warranty? If he does offer a one-year warranty? iii. Will Lew’s match Harry’s one-year warranty? iv. Is it a good idea for Harry to offer a one-year warranty?

b. What if Harry offers a two-year warranty? Will this offer generate a credible signal of quality? What about a three-year warranty?

c. If you were advising Harry, how long a warranty would you urge him to offer? Explain why.

Answer 1

(a)

The assumption that the person H is offering warranties, it tells that there is prevalent asymmetric information in the market and thus, the average price is $7,000.

(i)

Without Offering Warranty:

If person L does not provide any provide warranty, then his cost is only $5,000. Thus,

the profit is total revenue minus the total cost

and can be written as,

IIL= S 70005000

IL= $2,000

Profit for person L is denoted by n.

Thus, the profit is $2,000 if he does not provide any warranty.

With Offering Warranty:

Now, if person L provides a one-year warranty,

then it will cost him, s1,000Y = $1,000 and thus his

cost is increased by ss.000 + $1,000 = $6,000. As the consumers are not able to determine the quality of the car. They would be willing to pay $8,500 per car. The profit is total revenue minus the total cost and can be written as,

IL= S 85006000 IL=$ 2,500

Thus, the profit is $2,500 if he provides one

year warranty.

(ii)

Harry will earn normal profit whether Lew provides one-year warranty or not?

Does not offer one-year Warranty:

Person H's cost of production for maintaining a car is $8,000 and the cost of one-year warranty is S500Y =500 and sell the car for 10,000.

Its total cost is $ 8,500 and average price is $

10,000.

The profit he earns is the total revenue minus

the total cost and can be written as,

Iu= S 100008500

I= 1,500

Profit for Person H is denoted by ..

Thus, the profit is $1,500 if he does not

provide any warranty.

Does offer Warranty:

If person L does offer warranty person H would be able to sell his car for $8,500 and

the company will not earn any profit.

(iii) Person L will match person H's one-year

warranty if there is an increase in the profit.

(iv)

It is not a good idea for person H to offer one year warranty unless and until person L acts irrationally and not offer the one-year

warranty.

(b)

Yes, it will send a credible signal of quality.

Let us assume that the buyer has the

information whose car is of what quality and let's find out the profitability of the Harry's car.

Suppose consumers are willing to pay

$10,000. Thus, the total cost to Harry is

$8,000 + $500(2) =$9,000 and profits are $1,000.

If Harry is providing warranty 3 years, then the

cost is $8,000+ $500(3) = $9,500 and the profit is $ 500.

(c) Harry should provide warranty up to the number of years for which he earns normal profit. The profit can be determined from the following equation,

IT- TR-TC 0 = 100008000500 Y 500Y = 2,000

Y = 4

A

Thus, he can offer warranty up to 4 years.